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Mathematical Problems in Engineering
Volume 2010, Article ID 697687, 15 pages
Research Article

Parametric and Nonparametric Empirical Regression Models: Case Study of Copper Bromide Laser Generation

1Department of Applied Mathematics and Modeling, Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 24 Tzar Assen Street, 4000 Plovdiv, Bulgaria
2Department of Physics, Technical University of Sofia, Branch Plovdiv, 25 Tz. Djusstabanov Street, 4000 Plovdiv, Bulgaria

Received 26 December 2009; Accepted 2 March 2010

Academic Editor: J. Jiang

Copyright © 2010 S. G. Gocheva-Ilieva and I. P. Iliev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to model the output laser power of a copper bromide laser with wavelengths of 510.6 and 578.2 nm we have applied two regression techniques—multiple linear regression and multivariate adaptive regression splines. The models have been constructed on the basis of PCA factors for historical data. The influence of first- and second-order interactions between predictors has been taken into account. The models are easily interpreted and have good prediction power, which is established from the results of their validation. The comparison of the derived models shows that these based on multivariate adaptive regression splines have an advantage over the others. The obtained results allow for the clarification of relationships between laser generation and the observed laser input variables, for better determining their influence on laser generation, in order to improve the experimental setup and laser production technology. They can be useful for evaluation of known experiments as well as for prediction of future experiments. The developed modeling methodology is also applicable for a wide range of similar laser devices—metal vapor lasers and gas lasers.